Problem: Solve for $x$ and $y$ using elimination. ${-3x+3y = 12}$ ${3x-2y = -3}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x+3y = 12}\thinspace$ to find $x$ ${-3x + 3}{(9)}{= 12}$ $-3x+27 = 12$ $-3x+27{-27} = 12{-27}$ $-3x = -15$ $\dfrac{-3x}{{-3}} = \dfrac{-15}{{-3}}$ ${x = 5}$ You can also plug ${y = 9}$ into $\thinspace {3x-2y = -3}\thinspace$ and get the same answer for $x$ : ${3x - 2}{(9)}{= -3}$ ${x = 5}$